Finite Group DatabasebetaFinite Group Databasebeta| order | 2752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C43 ⋊ C2 |
| Sylow | C43 ⋊ #496 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D172 |
| commutator, cosocle | C2×C4×C43 | C23 |
| Frattini | C2×C4 | C22×D43 |
| Fitting | #97×C43 | C2 |
| socle | C22×C43 | C2×D4 |
| hypercenter | #97 | D43 |
| hypocenter | C43 | #496 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1376 |
Polycyclic presentation:
2^6,43|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^42,c^b=cf436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2752, 938);